It is known to equip round balers with a bale wrapping device, as a result of which a pressed bale is wrapped with a wrapping material and can then be ejected in wrapped form. The bale is brought into shape in a cylindrical pressing chamber of the round baler during a bale formation phase. For this purpose, crop lying on the ground is conveyed by a crop pick-up device into the pressing chamber and a cylindrical bale is shaped by arranged pressing means. The pressing chamber can be designed as a fixed pressing chamber, with cylindrically arranged pressing rollers, or else as a variable pressing chamber, with variable pressing means, for example pressing belts or pressing chains. In a wrapping material introduction phase following the bale formation phase, a wrapping material is guided from a wrapping material roll into the pressing chamber in the direction of the bale formed in the meantime and is entrained by the outer side of the bale. Wrapping material used is customarily mesh, film or twine. The rotating bale causes the wrapping material to be guided around the bale in a wrapping material wrapping phase. A wrapping material severing phase follows in which the wrapping material is severed from the bale by a cutting device before the bale is ejected in the bale ejection phase and deposited on the ground. It has turned out to be problematic to adapt the speed of the wrapping material roll to the individual phases and in particular also to allow a certain brake or acceleration force to act on the wrapping material roll such that there is an optimum wrapping material relief or wrapping material tightening for the corresponding phases. In the event of wrapping material relief and wrapping material tightening not being appropriately adapted to the phases, entanglements of the wrapping material with the pressing means or even defective wrapping material severings may occur, which, under some circumstances would interfere with or even interrupt the baling process. It is therefore sought to provide a bale wrapping device for a round baler, with which a round baler is operable with an optimizable wrapping material relief and with an optimizable wrapping material tightening in the individual phases mentioned of a baling process.